Stochastic processes associated with resistance forms

与阻力形式相关的随机过程

• 批准号: 19K03540
• 负责人: Croydon David
• 金额: $ 2.75万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2019
• 资助国家: 日本
• 起止时间: 2019-04-01 至 2024-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-19K03540/
• 关键词: Mott hopping; Extremal process; Random walk; Localization; Random environment; random walk; percolation; subdiffusion; trapping; hear kernel estimates; uniform spanning tree; critical dimension; Mott random walk; heat kernel estimates; scali

My main research achievement this year was the completion of a paper "Extremal regime for one-dimensional Mott variable-range hopping", jointly with Ryoki Fukushima and Stefan Junk. After the two-year period of limited research travel due to covid, I also restarted academic travels, making an extended trip to the the UK to work with Ben Hambly. I gave numerous research presentations around the UK, as well as ones in Germany and Mexico. The trip was a good chance to initiate collaborative projects.

我今年的主要研究成果是与 Ryoki Fukushima 和 Stefan Junk 合作完成了论文《Extremalregime for one-Dimensional Mott Variable-range hopping》。在因新冠疫情而受到限制的两年研究旅行之后，我也重新开始了学术旅行，并进行了一次长时间的英国旅行，与本·汉布利 (Ben Hambly) 一起工作。我在英国、德国和墨西哥做了许多研究报告。这次旅行是启动合作项目的好机会。

项目成果

Anomalous scaling regime for one-dimensional Mott variable-range hopping

一维 Mott 可变范围跳跃的反常缩放机制

• 发表时间: 2022
• 作者: David Croydon

Scaling limits of random walks on random graphs in critical regimes

关键状态下随机图上随机游走的缩放限制

• 发表时间: 2019
• 作者: David Croydon

Scaling limit for random walk on the range of random walk in four dimensions

四维随机游走范围上随机游走的尺度限制

• DOI: 10.1214/22-aihp1243
• 发表时间: 2023
• 作者: D. A. Croydon;D. Shiraishi
• 通讯作者: D. Shiraishi

Scaling limits of random walks on random graphs in critical regimes

关键状态下随机图上随机游走的缩放限制

• 发表时间: 2019
• 作者: David Croydon

Random walks on the two- and three-dimensional uniform spanning trees

二维和三维均匀生成树上的随机游走

• 发表时间: 2019
• 作者: David Croydon